A095306 Numbers k such that R(d) * 2^k + 1 is prime, where R() = A002275 and d is the number of decimal digits of 2^k.

1, 2, 5, 12, 19, 107, 117, 159, 217, 517, 868, 1412, 1636, 4051, 5965, 9128, 13857, 19611

Offset

1,2

Comments

a(1) through a(16) have been proved to be prime with WinPFGW. a(16) has 5495 digits. No more terms up to 11700.

Results were computed using the PrimeFormGW (PFGW) primality-testing program. - Hugo Pfoertner, Nov 14 2019

Links

Table of n, a(n) for n=1..18.

Example

a(5) = 19 is a term because 2^19 = 524288 has 6 digits and 111111 * 2^19 + 1 = 58254163969, a prime.

Crossrefs

Cf. A002275, A095967.

Sequence in context: A276478 A396397 A333558 * A356649 A258602 A327065

Adjacent sequences: A095303 A095304 A095305 * A095307 A095308 A095309

Keyword

nonn,base,hard,more

Author

Jason Earls, Jul 13 2004

Extensions

a(17)-a(18) from Michael S. Branicky, Feb 08 2026

Status

approved